Theorems · Theorem · linear algebra

Module.DualBases.lc_coeffs

∀ {R : Type u_1} {M : Type u_2} {ι : Type u_3} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  {e : ι → M} {ε : ι → Module.Dual R M} (h : Module.DualBases e ε) (m : M), Module.DualBases.lc e (h.coeffs m) = m

For any m : M n, $\sum_{p ∈ Q n} (ε p m) • e p = m$

Defined in

Mathlib.LinearAlgebra.Dual.Basis

Cited by

0 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModule